hdmi playback review hdtv

New camera arrived focussed for selfies, partly fixed after massive glue removal job (glued in 3 places, each with huge blobs of glue - compared to online illustrations - forced between lens and lens mount) that took almost an hour to remove. HDMI connection to monitor checked, worked...

If we record with the cam and connect to a hdtv via hdmi, why can't we playback our footages? I don't see the point. Why is the hdmi connector on it? Only for live viewing? Oh yes, for focus adjusting :( But i thinked, most people like or think to use this connector for reviewing footages. Why...